# Forum for Science, Industry and Business

Search our Site:

## What does a basket of shares cost? Researcher works it out.

05.06.2008
Dutch researcher Coen Leentvaar has been studying the problem that arises if options have to be priced on a number of shares.

From an arithmetical standpoint, the question introduces so many unknown variables that even a modern computer cannot handle the calculation. As part of a Technology Foundation STW project, Leentvaar split the problem into a number of less complex partial problems. He also developed an algorithm that, combined with computer technology, can calculate the option price for a basket of shares.

Using a computer, it is hard to determine the option price for a variety of shares. The multitude of possibilities mean the number of unknowns to be resolved grows exponentially. For example, an option on a basket of five shares involves 32 million unknowns, given a 32-point grid. This is beyond the capabilities of today’s computer systems. Leentvaar used the so-called thin-grid method to split the problem into a number of less complex partial problems that could be handled by a modern computer system. The option price can be estimated accurately by combining the solutions of all the partial problems in the correct manner.

However, the option contract has one annoying feature if the thin-grid method is used, namely it is not always advantageous to exercise an option (i.e. to exercise the right to buy or sell at a particular time). Mathematically, this leads to a ‘kink’ in the final solution to the problem. Leentvaar used variable transforms to minimise this ‘kink’, so that it is dependent on only one variable: the value of the basket itself. The thin-grid method can be used with reasonable accuracy by calculating this particular variable more precisely and the other variables more coarsely.

This leaves the options based on the worst- or best-performing share. These options do not lend themselves to solution using differential equations because the preconditions are missing. Leentvaar used advanced parallelisation methods (Fourier transforms) for this purpose. By cleverly splitting up the problem, these methods are able to solve each part independently of the rest. In this way, the researcher managed to combine the power of the thin-grid method with the parallelisation of the Fourier transforms into a computer model that divides a large problem into many small parts and then solves these.

Trade in underlying futures, or hedging, is based on derivatives of the option prices. This either cannot be done accurately enough using current methods or there is no reference. Leentvaar’s method is one where the derivatives, or Greeks, can easily be determined on the basis of the calculated prices. This offers the prospect of further research into making pricing methods more efficient. Participating organisations are ABN-AMRO, Rabobank, Binck (formerly AOT) and Tilburg University.

David Redeker | alfa
Further information:
http://www.nwo.nl/nwohome.nsf/pages/NWOA_7F2GP6_Eng

### More articles from Business and Finance:

Microtechnology industry is hiring – positive developments of past years continue
09.04.2018 | IVAM Fachverband für Mikrotechnik

RWI/ISL-Container Throughput Index with minor decline on a high overall level
20.03.2018 | RWI – Leibniz-Institut für Wirtschaftsforschung

### Im Focus: Fraunhofer IDMT demonstrates its method for acoustic quality inspection at »Sensor+Test 2019« in Nürnberg

From June 25th to 27th 2019, the Fraunhofer Institute for Digital Media Technology IDMT in Ilmenau (Germany) will be presenting a new solution for acoustic quality inspection allowing contact-free, non-destructive testing of manufactured parts and components. The method which has reached Technology Readiness Level 6 already, is currently being successfully tested in practical use together with a number of industrial partners.

Reducing machine downtime, manufacturing defects, and excessive scrap

### Im Focus: Successfully Tested in Praxis: Bidirectional Sensor Technology Optimizes Laser Material Deposition

The quality of additively manufactured components depends not only on the manufacturing process, but also on the inline process control. The process control ensures a reliable coating process because it detects deviations from the target geometry immediately. At LASER World of PHOTONICS 2019, the Fraunhofer Institute for Laser Technology ILT will be demonstrating how well bi-directional sensor technology can already be used for Laser Material Deposition (LMD) in combination with commercial optics at booth A2.431.

Fraunhofer ILT has been developing optical sensor technology specifically for production measurement technology for around 10 years. In particular, its »bd-1«...

### Im Focus: The hidden structure of the periodic system

The well-known representation of chemical elements is just one example of how objects can be arranged and classified

The periodic table of elements that most chemistry books depict is only one special case. This tabular overview of the chemical elements, which goes back to...

### Im Focus: MPSD team discovers light-induced ferroelectricity in strontium titanate

Light can be used not only to measure materials’ properties, but also to change them. Especially interesting are those cases in which the function of a material can be modified, such as its ability to conduct electricity or to store information in its magnetic state. A team led by Andrea Cavalleri from the Max Planck Institute for the Structure and Dynamics of Matter in Hamburg used terahertz frequency light pulses to transform a non-ferroelectric material into a ferroelectric one.

Ferroelectricity is a state in which the constituent lattice “looks” in one specific direction, forming a macroscopic electrical polarisation. The ability to...

### Im Focus: Determining the Earth’s gravity field more accurately than ever before

Researchers at TU Graz calculate the most accurate gravity field determination of the Earth using 1.16 billion satellite measurements. This yields valuable knowledge for climate research.

The Earth’s gravity fluctuates from place to place. Geodesists use this phenomenon to observe geodynamic and climatological processes. Using...

All Focus news of the innovation-report >>>

Anzeige

Anzeige